Rudy, worry? About Rick who? The question centers on the latest in a series of events that have shaken the air of inevitability around Mayor Giuliani's much-vaunted but still-only-presumed Senate run against Hillary Rodham Clinton.

This week, Long Island Congressman Rick Lazio, a dark-horse moderate, announced he's ready to jump in and challenge the mayor in the Republican primary. The reason: The mayor's poll numbers are slipping with key constituencies, as his handling of the fourth police shooting of an unarmed black man in just over a year has again raised questions about his temperament.

"Rudy is not finished by any stretch," says pollster John Zogby. "But he has now revealed to the nation and to the state some character flaws.... The question is, how does he deal with those? If he continues down the road he's on, then those character flaws become a dominant issue."

While campaigning on Long Island with Arizona Sen. John McCain on Tuesday, the mayor retained his characteristic confidence. He dismissed Representative Lazio's ambitions, saying, "If he wants to run, he should, and we'll have a primary."

The mayor also made light of his renowned, but sometimes pugnacious demeanor. When a woman in the audience at the veterans' hall noted that Mrs. Clinton has charged he doesn't have the temperament to be in the Senate, Giuliani looked suddenly stern, and shot back: "Did she say that? Sit down! Shut up!," mocking himself as the crowd laughed. Then he added. "I'm very forceful in my advocacy. Maybe Washington needs a little of that." Senator McCain concurred, saying he needed a "soulmate" in the Senate.

Yet the mayor also refused to back down or show remorse for his controversial handling of the fatal shooting of Patrick Dorismond, an unarmed security guard caught in a botched drug sting last month, including his decision to release Mr. Dorismond's sealed juvenile-court records.

"Once a grand jury [and] all that happens, there'll be a different view of it," he told reporters, rolling along in a New York version of McCain's "Straight Talk Express."

But the controversy has had an effect on Giuliani's standing with voters. While the race remains in a statistical dead heat, Giuliani slipped behind Clinton for the first time in months in at least one poll. Political scientist Esther Fuchs of New York's Barnard College says that what's stunning is not the neck-and-neck nature of the race, but how various constituencies within it are shifting.

"Before, Giuliani had 42 percent support in the Jewish community and she had 51 percent," says Ms. Fuchs. "But in the recent Zogby poll, his support went down to 28 percent and hers went up to 56 percent. He's been targeting the Jewish Democratic vote, and I believe it's now gone."

Fuchs says that because both candidates have very high negative poll numbers, their support is very soft. That's also given fuel to Lazio and his supporters. At a press conference this week, Lazio said the campaign has degenerated into a personality contest.

"It sells copy, but it's not good for the people of New York," he said.

Lazio also noted that Giuliani will not win the backing of the Conservative Party, a key constituency. No New York Republican has been able to win a statewide office without its endorsement since 1974.

"The fact is that Giuliani is not the darling of the conservative wing of his party and those people aren't going to go away," says Helen DesFosses, a political scientist at the State University of New York in Albany. "I think they're going to have to make some concessions to conservatives to get Lazio to fade out of sight."

But Michael Long, chairman of the Conservative Party is not interested in having Lazio fade out. In fact, he said, if the congressman announces his candidacy, he'd throw his support behind him: "I believe he better reflects the views of the average Republicans throughout the state of New York. He doesn't have the mayor's high negatives, and he makes the perfect candidate to beat Hillary Clinton."

Many pundits agree with that assessment. But others believe the mayor has something the little-known congressman from Long Island lacks: winnability.

"Mrs. Clinton running has struck fear and loathing into the hearts of Republican primary voters, who now believe they don't have the luxury of voting for a Rick Lazio, even though they are more allied and compatible with him. These people are focusing on one thing: winnability," says Jay Severin, a New York-based GOP political consultant.